The first time David Montgomery meets someone, the Phillies’ chairman always has one request.

Rather than Mr. Montgomery, call him David.

“And some people don’t do that but most will,” Montgomery says. “I just want people to know we’re not on different levels. We all work for the Phillies.”

Relationship building and taking a vested interest in Phillies employees — from ushers to the bat boy to members of the front office and everyone in between — is a defining characteristic of Montgomery. The Phillies have cultivated a culture synonymous with loyalty and family. Montgomery takes pride in it.

“We’re a service organization and our job is to treat our customers well,” Montgomery says. “Well, the best way to treat your customers well is to treat your employees well. And one of the best ways you can show your employees is you care about them as people as opposed to just a...